Distinguishing Number of Countable Homogeneous Relational Structures

Details Distinguishing Number of Countable Homogeneous Relational Structures Distinguishing Number of Countable Homogeneous Relational Structures

2008-04-24

arxiv.org/abs/0804.4019v1

Mathematics

Logic

21 pages

Scientific paper

The distinguishing number of a graph $G$ is the smallest positive integer $r$ such that $G$ has a labeling of its vertices with $r$ labels for which there is no non-trivial automorphism of $G$ preserving these labels. Albertson and Collins computed the distinguishing number for various finite graphs, and Imrich, Klav\v{z}ar and Trofimov computed the distinguishing number of some infinite graphs, showing in particular that the Random Graph has distinguishing number 2. We compute the distinguishing number of various other finite and countable homogeneous structures, including undirected and directed graphs, and posets. We show that this number is in most cases two or infinite, and besides a few exceptions conjecture that this is so for all primitive homogeneous countable structures.

Affiliated with

Also associated with

No associations

Rating

Distinguishing Number of Countable Homogeneous Relational Structures does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Distinguishing Number of Countable Homogeneous Relational Structures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Distinguishing Number of Countable Homogeneous Relational Structures will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-728062